Approach to mathematical modeling of the process of carcinogenesis

Background. The steady increase in the incidence and mortality rates of malignant neoplasms necessitates the integration of advanced high-tech research methods into oncology, one of which is mathematical modeling of the initiation, promotion, and progression of malignant tumors. The complexity of mathematical modeling of carcinogenesis is associated with the need to consider a significant number of factors influencing this process, as well as its specificity, multi-level nature, multi-stage progression, and varying scales. A detailed study of the molecular mechanisms underlying the process of carcinogenesis is essential for developing new approaches to describing and modeling the process of cell malignancy. Purpose – of the study is to conduct a comparative analysis of existing mathematical models of the cell malignancy process and the development of oncological diseases, as well as mathematical methods for predicting the dynamics of biological systemsʼ behavior in various types of cells during their interaction. This is intended to optimize the processes of cancer detection and treatment. Materials and Methods. The study involves an analysis of scientific data on mathematical modeling in biology and medicine, particularly in oncology, through a review of available domestic and international scientific literature. Results. The study examined the specific features of the pathogenesis of oncological diseases that must be considered in mathematical modeling of this process. It was demonstrated that mathematical modeling of biological processes has its unique characteristics, and the importance of selecting appropriate mathematical methods and tools in accordance with the modeling objectives was highlighted. A deterministic model describing the interaction between malignant tumor cells and immune cells of the body was analyzed, and its limitations were identified. Evidence supporting the necessity of employing a probabilistic approach to describe the process of carcinogenesis was presented. Conclusions. The correct choice of a mathematical modeling method for the processes of initiation, promotion, and progression of malignant tumors represents a powerful modern scientific approach to studying the etiology and development of oncological diseases. The application of mathematical modeling in oncology improves the understanding of hidden clinical patterns, enhances disease diagnosis, and enables better forecasting of disease progression, ultimately optimizing treatment strategies for cancer patients.